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• Vl-immdepgraph

Vl-immdepgraph-fix

Fixing function for vl-immdepgraph structures.

Signature

(vl-immdepgraph-fix x) → new-x

Arguments

x — Guard (vl-immdepgraph-p x).

Returns

new-x — Type (vl-immdepgraph-p new-x).

Definitions and Theorems

Function: vl-immdepgraph-fix$inline

(defun vl-immdepgraph-fix$inline (x)
 (declare (xargs :guard (vl-immdepgraph-p x)))
 (let ((__function__ 'vl-immdepgraph-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((all-okp (acl2::bool-fix (std::prod-car (cdr x))))
     (deps
          (vl-depgraph-fix (std::prod-car (std::prod-cdr (cdr x)))))
     (reportcard
       (vl-reportcard-fix (std::prod-cdr (std::prod-cdr (cdr x))))))
    (cons :vl-immdepgraph
          (std::prod-cons all-okp
                          (std::prod-cons deps reportcard))))
   :exec x)))

Theorem: vl-immdepgraph-p-of-vl-immdepgraph-fix

(defthm vl-immdepgraph-p-of-vl-immdepgraph-fix
  (b* ((new-x (vl-immdepgraph-fix$inline x)))
    (vl-immdepgraph-p new-x))
  :rule-classes :rewrite)

Theorem: vl-immdepgraph-fix-when-vl-immdepgraph-p

(defthm vl-immdepgraph-fix-when-vl-immdepgraph-p
  (implies (vl-immdepgraph-p x)
           (equal (vl-immdepgraph-fix x) x)))

Function: vl-immdepgraph-equiv$inline

(defun vl-immdepgraph-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (vl-immdepgraph-p acl2::x)
                              (vl-immdepgraph-p acl2::y))))
  (equal (vl-immdepgraph-fix acl2::x)
         (vl-immdepgraph-fix acl2::y)))

Theorem: vl-immdepgraph-equiv-is-an-equivalence

(defthm vl-immdepgraph-equiv-is-an-equivalence
  (and (booleanp (vl-immdepgraph-equiv x y))
       (vl-immdepgraph-equiv x x)
       (implies (vl-immdepgraph-equiv x y)
                (vl-immdepgraph-equiv y x))
       (implies (and (vl-immdepgraph-equiv x y)
                     (vl-immdepgraph-equiv y z))
                (vl-immdepgraph-equiv x z)))
  :rule-classes (:equivalence))

Theorem: vl-immdepgraph-equiv-implies-equal-vl-immdepgraph-fix-1

(defthm vl-immdepgraph-equiv-implies-equal-vl-immdepgraph-fix-1
  (implies (vl-immdepgraph-equiv acl2::x x-equiv)
           (equal (vl-immdepgraph-fix acl2::x)
                  (vl-immdepgraph-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vl-immdepgraph-fix-under-vl-immdepgraph-equiv

(defthm vl-immdepgraph-fix-under-vl-immdepgraph-equiv
  (vl-immdepgraph-equiv (vl-immdepgraph-fix acl2::x)
                        acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-vl-immdepgraph-fix-1-forward-to-vl-immdepgraph-equiv

(defthm
      equal-of-vl-immdepgraph-fix-1-forward-to-vl-immdepgraph-equiv
  (implies (equal (vl-immdepgraph-fix acl2::x)
                  acl2::y)
           (vl-immdepgraph-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-vl-immdepgraph-fix-2-forward-to-vl-immdepgraph-equiv

(defthm
      equal-of-vl-immdepgraph-fix-2-forward-to-vl-immdepgraph-equiv
  (implies (equal acl2::x (vl-immdepgraph-fix acl2::y))
           (vl-immdepgraph-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: vl-immdepgraph-equiv-of-vl-immdepgraph-fix-1-forward

(defthm vl-immdepgraph-equiv-of-vl-immdepgraph-fix-1-forward
  (implies (vl-immdepgraph-equiv (vl-immdepgraph-fix acl2::x)
                                 acl2::y)
           (vl-immdepgraph-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: vl-immdepgraph-equiv-of-vl-immdepgraph-fix-2-forward

(defthm vl-immdepgraph-equiv-of-vl-immdepgraph-fix-2-forward
  (implies
       (vl-immdepgraph-equiv acl2::x (vl-immdepgraph-fix acl2::y))
       (vl-immdepgraph-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)